Bose-glass to Superfluid transition in the three-dimensional Bose-Hubbard Model

TL;DR

This study uses Monte Carlo simulations to analyze the quantum phase transition from Bose-glass to superfluid in a 3D Bose-Hubbard model, focusing on critical exponents and correlation functions.

Contribution

It provides the first detailed finite-size scaling analysis of this transition using a (3+1)D link-current model with the geometrical worm algorithm.

Findings

Critical dynamical exponent z = 3 consistent with theory.

Correlation length exponent ν ≈ 0.70, satisfying scaling relations.

Discrepancies in correlation functions suggest finite-size effects or non-asymptotic behavior.

Abstract

We present a Monte Carlo study of the Bose-glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3 + 1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as 16x16x16x512 sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z = 3, in agreement with existing scaling and renormalization group arguments that z = d. We find also a value of $\nu = 0.70(12)$ for the correlation length exponent, satisfying the relation $\nu >= 2/d$. However, a detailed study of the correlation functions, C(r, tau), at the quantum critical point are not consistent with this value of z. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.